Example of Inverse Laplace Transform
Example 1: Given the Laplace transform , find the inverse Laplace transform.
Decompose \( F(s) \) into partial fractions:
Solving for ( A ) and ( B ), you get ( A = i ) and ( B = -i ).
The inverse Laplace transform of is eat, so for and , the inverse transforms are Ae2it and Be-2it respectively.
Combine the results to get the overall inverse Laplace transform:
Example 2: Given , find the inverse Laplace transform.
Factorize the denominator and complete the square:
s2 + 2s + 5 = (s+1)2 + 4
Decompose (G(s)) into partial fractions:
Solve for the constants to get ( A = 3 ) and ( B = -1 ).
The inverse Laplace transform of is , so for and , the inverse transforms are and respectively.
Combine the results to get the overall inverse Laplace transform:
Inverse Laplace Transform
In this Article, We will be going through the Inverse Laplace transform, We will start our Article with an introduction to the basics of the Laplace Transform, Then we will go through the Inverse Laplace Transform, will see its Basic Properties, Inverse Laplace Table for some Functions, We will also see the Difference between Laplace Transform and Inverse Laplace Transform, At last, we will conclude our Article with Some examples of inverse Laplace Transform, Applications of inverse Laplace and Some FAQs.
Table of Content
- Inverse Laplace Transform
- Inverse Laplace Transform Theorem
- Inverse Laplace Transform Table
- Laplace Transform Vs Inverse Laplace Transform
- Properties
- Advantages and Disadvantages
- Applications
- Examples